SOLUTION: In the xy-plane, line "l" passes through the origin and is perpendicular to the line 4x+y=k, where k is a constant. If the two lines intersect at point (t, t+1), what is the value

Algebra ->  Algebra  -> College  -> Linear Algebra -> SOLUTION: In the xy-plane, line "l" passes through the origin and is perpendicular to the line 4x+y=k, where k is a constant. If the two lines intersect at point (t, t+1), what is the value      Log On


   

Question 470538: In the xy-plane, line "l" passes through the origin and is perpendicular to the line 4x+y=k, where k is a constant. If the two lines intersect at point (t, t+1), what is the value of t?
The answer is -4/3, but I am not sure how to get this answer? Please help.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
changing to slope-intercept, the given line becomes ___ y = -4x + k (the slope being -4)

since perpendicular lines have negative-reciprocal slopes, the equation of "l" is ___ y = (1/4)x
___ the constant, intercept, term is zero because the line goes through the origin

substituting ___ (t + 1) = (t) / 4

4t + 4 = t